In [56]:
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
import pmdarima as pm
from statsmodels.tsa.arima_model import ARIMA
from sklearn.metrics import mean_squared_error
from math import sqrt, ceil
sns.set_theme()
Temporal Modelling (ARIMA)¶
In this notebook we apply an ARIMA model to the 3 datasets, and attempt to predict the last 30 days in the dataset. First we define the fitting and plotting functions we will use for all datasets. We utilize the pmdarima package for fitting and forecasting, and Seaborn for plotting the results.
In [61]:
def autoARIMAfunc(df):
# Training data split
train_df = df.iloc[:-30]
test_df = df.iloc[-30:]
# define output dataframes
forecast_df = pd.DataFrame(index = test_df.index)
upper_df = pd.DataFrame(index = test_df.index)
lower_df = pd.DataFrame(index = test_df.index)
fit_df = pd.DataFrame(index = train_df.index)
columns = df.columns
for col in columns[1:]:
# apply auto_arima. will estimate the pdq x PDQ model paramenters
model = pm.auto_arima(train_df[col], seasonal=True, start_p=0, start_q=0, max_p=10, max_q=10, trace=True)
# generate forecast and confidence intervals
forecast, confidenceInt = model.predict(30, return_conf_int=True)
forecast_df[col] = forecast
lower_df[col] = confidenceInt[:,0]
upper_df[col] = confidenceInt[:,1]
fit_df[col] = model.fittedvalues()
return train_df, test_df, fit_df, forecast_df, lower_df, upper_df
In [62]:
def plotARIMAfunc(train_df, test_df, fit_df, forecast_df, lower_df, upper_df):
columns = train_df.columns
k = ceil(len(columns)/2)
fig, axs = plt.subplots(nrows=k, ncols=2, figsize=(30, k*5))
i = 0
j = 0
palette = sns.color_palette()
for col in columns[1:]:
# Plot data and fitted model
sns.lineplot(x = train_df.timestamp.iloc[-300:], y = train_df[col].iloc[-300:], ax=axs[i,j], color=palette[0], label="Actual")
sns.lineplot(x = train_df.timestamp.iloc[-300:], y = fit_df[col].iloc[-300:], ax=axs[i,j], color=palette[1], label="Forecast")
sns.lineplot(x = test_df.timestamp, y = test_df[col], ax=axs[i,j], color=palette[0])
sns.lineplot(x = test_df.timestamp, y = forecast_df[col], ax=axs[i,j], color=palette[1])
# plot confidence interval
axs[i,j].fill_between(test_df.timestamp, lower_df[col], upper_df[col], alpha=0.2)
# print RMSE, and add legend and labels
rmse = sqrt(mean_squared_error(test_df[col], forecast_df[col]))
print(f'RMSE for {col} Stations: {rmse}')
axs[i,j].set_title(col + f", Forecast RMSE: {rmse}")
axs[i,j].set_xlabel('')
axs[i,j].set_ylabel('Energy (kWh)')
axs[i,j].legend(loc='upper left')
j += 1
if j >= 2:
i += 1
j = 0
plt.show()
Palo Alto¶
In [57]:
PA_data = pd.read_csv('data/EVChargingStationUsage.csv')
C:\Users\pgsva\AppData\Local\Temp\ipykernel_15248\1309580590.py:1: DtypeWarning: Columns (29,30,32) have mixed types. Specify dtype option on import or set low_memory=False.
PA_data = pd.read_csv('data/EVChargingStationUsage.csv')
In [58]:
# format station names to merge chargers at same location
PA_data["Normalized Station Name"] = PA_data["Station Name"].str.split(pat=" / | #| [0-9]").apply(lambda col: col[1])
PA_data.dropna(subset=['Normalized Station Name'], inplace=True)
In [59]:
# transform timestamp to Datetime object and simplify to dates
PA_data = PA_data.assign(timestamp=pd.to_datetime(PA_data["Transaction Date (Pacific Time)"], format="%m/%d/%Y %H:%M", errors='coerce').dt.date)
# group energy consumption around dates and station
PA_data = PA_data[["timestamp", "Normalized Station Name", "Energy (kWh)"]].groupby(["timestamp", "Normalized Station Name"], as_index=False).sum()
# Pivot energy consumption data to have rows indexed on dates and columns indexed on stations
PA_data = pd.pivot_table(PA_data, values="Energy (kWh)", index="timestamp", columns= "Normalized Station Name", aggfunc=np.sum, fill_value=0)
PA_data.reset_index(inplace=True)
To understand the shortcomings of the datasets we identify the number of dates with no charging data for a given station
In [60]:
print(PA_data[PA_data == 0].count(axis=0)/len(PA_data.index))
Normalized Station Name timestamp 0.000000 BRYANT 0.033382 CAMBRIDGE 0.476343 HAMILTON 0.020900 HIGH 0.027866 MPL 0.340784 RINCONADA LIB 0.418578 SHERMAN 0.994485 TED THOMPSON 0.479245 WEBSTER 0.427286 dtype: float64
In [63]:
train_df_PA, test_df_PA, fit_df_PA, forecast_df_PA, lower_df_PA, upper_df_PA = autoARIMAfunc(PA_data)
Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=37372.727, Time=0.15 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=36960.169, Time=0.27 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=36146.508, Time=0.88 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=37370.730, Time=0.08 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=35994.253, Time=1.67 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=35979.611, Time=2.65 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=36761.400, Time=0.44 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=35933.462, Time=3.16 sec ARIMA(3,1,0)(0,0,0)[0] intercept : AIC=36547.572, Time=0.52 sec ARIMA(4,1,1)(0,0,0)[0] intercept : AIC=35900.502, Time=4.09 sec ARIMA(4,1,0)(0,0,0)[0] intercept : AIC=36430.061, Time=0.82 sec ARIMA(5,1,1)(0,0,0)[0] intercept : AIC=35693.881, Time=4.32 sec ARIMA(5,1,0)(0,0,0)[0] intercept : AIC=36037.299, Time=0.95 sec ARIMA(6,1,1)(0,0,0)[0] intercept : AIC=35440.340, Time=6.66 sec ARIMA(6,1,0)(0,0,0)[0] intercept : AIC=35439.026, Time=1.60 sec ARIMA(7,1,0)(0,0,0)[0] intercept : AIC=35440.092, Time=1.78 sec ARIMA(7,1,1)(0,0,0)[0] intercept : AIC=35440.609, Time=5.29 sec ARIMA(6,1,0)(0,0,0)[0] : AIC=35437.049, Time=0.78 sec ARIMA(5,1,0)(0,0,0)[0] : AIC=36035.312, Time=0.48 sec ARIMA(7,1,0)(0,0,0)[0] : AIC=35438.115, Time=0.93 sec ARIMA(6,1,1)(0,0,0)[0] : AIC=35438.363, Time=3.26 sec ARIMA(5,1,1)(0,0,0)[0] : AIC=35691.891, Time=1.97 sec ARIMA(7,1,1)(0,0,0)[0] : AIC=35438.629, Time=2.49 sec Best model: ARIMA(6,1,0)(0,0,0)[0] Total fit time: 45.255 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=35638.486, Time=0.15 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=35263.798, Time=0.33 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=34514.366, Time=0.81 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=35636.491, Time=0.09 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=34338.900, Time=1.25 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=34318.303, Time=2.05 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=35032.734, Time=0.46 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=34295.910, Time=3.43 sec ARIMA(3,1,0)(0,0,0)[0] intercept : AIC=34900.077, Time=0.56 sec ARIMA(4,1,1)(0,0,0)[0] intercept : AIC=34229.779, Time=3.91 sec ARIMA(4,1,0)(0,0,0)[0] intercept : AIC=34759.672, Time=0.77 sec ARIMA(5,1,1)(0,0,0)[0] intercept : AIC=34049.714, Time=5.08 sec ARIMA(5,1,0)(0,0,0)[0] intercept : AIC=34390.971, Time=0.91 sec ARIMA(6,1,1)(0,0,0)[0] intercept : AIC=33695.646, Time=6.24 sec ARIMA(6,1,0)(0,0,0)[0] intercept : AIC=33704.758, Time=1.49 sec ARIMA(7,1,1)(0,0,0)[0] intercept : AIC=33688.109, Time=7.12 sec ARIMA(7,1,0)(0,0,0)[0] intercept : AIC=33693.003, Time=1.46 sec ARIMA(8,1,1)(0,0,0)[0] intercept : AIC=33686.721, Time=10.80 sec ARIMA(8,1,0)(0,0,0)[0] intercept : AIC=33685.744, Time=2.01 sec ARIMA(9,1,0)(0,0,0)[0] intercept : AIC=33684.834, Time=5.56 sec ARIMA(10,1,0)(0,0,0)[0] intercept : AIC=33678.613, Time=6.95 sec ARIMA(10,1,1)(0,0,0)[0] intercept : AIC=33620.929, Time=18.37 sec ARIMA(9,1,1)(0,0,0)[0] intercept : AIC=33639.145, Time=15.55 sec ARIMA(10,1,2)(0,0,0)[0] intercept : AIC=33621.949, Time=20.84 sec ARIMA(9,1,2)(0,0,0)[0] intercept : AIC=33621.441, Time=19.53 sec ARIMA(10,1,1)(0,0,0)[0] : AIC=33619.085, Time=6.95 sec ARIMA(9,1,1)(0,0,0)[0] : AIC=33637.337, Time=6.73 sec ARIMA(10,1,0)(0,0,0)[0] : AIC=33676.669, Time=2.96 sec ARIMA(10,1,2)(0,0,0)[0] : AIC=33620.103, Time=9.77 sec ARIMA(9,1,0)(0,0,0)[0] : AIC=33682.888, Time=2.57 sec ARIMA(9,1,2)(0,0,0)[0] : AIC=33619.492, Time=9.45 sec Best model: ARIMA(10,1,1)(0,0,0)[0] Total fit time: 174.174 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=34402.789, Time=0.17 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=33665.912, Time=0.29 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=32640.865, Time=0.81 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=34400.789, Time=0.08 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=32617.529, Time=1.47 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=32618.308, Time=2.11 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=32644.473, Time=2.37 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=32617.125, Time=1.37 sec ARIMA(0,1,3)(0,0,0)[0] intercept : AIC=32619.060, Time=2.61 sec ARIMA(1,1,3)(0,0,0)[0] intercept : AIC=32621.084, Time=4.25 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=32615.139, Time=0.70 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=32638.880, Time=0.33 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=32642.488, Time=1.19 sec ARIMA(0,1,3)(0,0,0)[0] : AIC=32617.074, Time=1.04 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=32615.543, Time=0.64 sec ARIMA(1,1,3)(0,0,0)[0] : AIC=32619.114, Time=1.59 sec Best model: ARIMA(0,1,2)(0,0,0)[0] Total fit time: 21.043 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=38294.451, Time=0.18 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=37766.676, Time=0.28 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=36777.417, Time=0.82 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=38292.451, Time=0.06 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=36708.879, Time=1.49 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=36691.628, Time=2.37 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=37466.409, Time=0.45 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=36678.557, Time=3.15 sec ARIMA(3,1,0)(0,0,0)[0] intercept : AIC=37270.389, Time=0.53 sec ARIMA(4,1,1)(0,0,0)[0] intercept : AIC=36665.539, Time=4.72 sec ARIMA(4,1,0)(0,0,0)[0] intercept : AIC=37178.309, Time=0.79 sec ARIMA(5,1,1)(0,0,0)[0] intercept : AIC=36581.019, Time=5.09 sec ARIMA(5,1,0)(0,0,0)[0] intercept : AIC=36885.907, Time=0.97 sec ARIMA(6,1,1)(0,0,0)[0] intercept : AIC=36517.437, Time=9.03 sec ARIMA(6,1,0)(0,0,0)[0] intercept : AIC=36540.724, Time=1.54 sec ARIMA(7,1,1)(0,0,0)[0] intercept : AIC=36466.824, Time=10.24 sec ARIMA(7,1,0)(0,0,0)[0] intercept : AIC=36512.854, Time=1.66 sec ARIMA(8,1,1)(0,0,0)[0] intercept : AIC=36462.998, Time=11.50 sec ARIMA(8,1,0)(0,0,0)[0] intercept : AIC=36512.470, Time=1.98 sec ARIMA(9,1,1)(0,0,0)[0] intercept : AIC=36443.449, Time=13.92 sec ARIMA(9,1,0)(0,0,0)[0] intercept : AIC=36511.658, Time=2.72 sec ARIMA(10,1,1)(0,0,0)[0] intercept : AIC=36441.011, Time=16.28 sec ARIMA(10,1,0)(0,0,0)[0] intercept : AIC=36513.583, Time=2.63 sec ARIMA(10,1,2)(0,0,0)[0] intercept : AIC=36435.060, Time=21.68 sec ARIMA(9,1,2)(0,0,0)[0] intercept : AIC=36432.062, Time=17.62 sec ARIMA(8,1,2)(0,0,0)[0] intercept : AIC=36454.681, Time=12.32 sec ARIMA(9,1,3)(0,0,0)[0] intercept : AIC=36398.116, Time=21.19 sec ARIMA(8,1,3)(0,0,0)[0] intercept : AIC=36450.909, Time=15.23 sec ARIMA(10,1,3)(0,0,0)[0] intercept : AIC=36434.817, Time=21.26 sec ARIMA(9,1,4)(0,0,0)[0] intercept : AIC=36398.719, Time=20.11 sec ARIMA(8,1,4)(0,0,0)[0] intercept : AIC=inf, Time=19.21 sec ARIMA(10,1,4)(0,0,0)[0] intercept : AIC=36441.275, Time=24.10 sec ARIMA(9,1,3)(0,0,0)[0] : AIC=36392.599, Time=11.44 sec ARIMA(8,1,3)(0,0,0)[0] : AIC=36448.939, Time=7.70 sec ARIMA(9,1,2)(0,0,0)[0] : AIC=36430.020, Time=8.52 sec ARIMA(10,1,3)(0,0,0)[0] : AIC=36432.887, Time=9.03 sec ARIMA(9,1,4)(0,0,0)[0] : AIC=36296.187, Time=11.57 sec ARIMA(8,1,4)(0,0,0)[0] : AIC=inf, Time=10.89 sec ARIMA(10,1,4)(0,0,0)[0] : AIC=36439.024, Time=10.52 sec ARIMA(9,1,5)(0,0,0)[0] : AIC=36222.548, Time=11.99 sec ARIMA(8,1,5)(0,0,0)[0] : AIC=36247.898, Time=10.32 sec ARIMA(10,1,5)(0,0,0)[0] : AIC=36220.938, Time=13.14 sec ARIMA(10,1,6)(0,0,0)[0] : AIC=36214.635, Time=14.26 sec ARIMA(9,1,6)(0,0,0)[0] : AIC=36230.296, Time=11.82 sec ARIMA(10,1,7)(0,0,0)[0] : AIC=36207.271, Time=14.70 sec ARIMA(9,1,7)(0,0,0)[0] : AIC=36196.260, Time=12.59 sec ARIMA(8,1,7)(0,0,0)[0] : AIC=36151.111, Time=13.08 sec ARIMA(7,1,7)(0,0,0)[0] : AIC=36134.652, Time=13.16 sec ARIMA(6,1,7)(0,0,0)[0] : AIC=inf, Time=12.34 sec ARIMA(7,1,6)(0,0,0)[0] : AIC=36109.126, Time=9.91 sec ARIMA(6,1,6)(0,0,0)[0] : AIC=inf, Time=9.58 sec ARIMA(7,1,5)(0,0,0)[0] : AIC=inf, Time=15.09 sec ARIMA(8,1,6)(0,0,0)[0] : AIC=36220.666, Time=11.26 sec ARIMA(6,1,5)(0,0,0)[0] : AIC=36108.985, Time=9.14 sec ARIMA(5,1,5)(0,0,0)[0] : AIC=36098.519, Time=8.86 sec ARIMA(4,1,5)(0,0,0)[0] : AIC=36105.079, Time=6.78 sec ARIMA(5,1,4)(0,0,0)[0] : AIC=36436.173, Time=6.58 sec ARIMA(5,1,6)(0,0,0)[0] : AIC=36083.979, Time=9.92 sec ARIMA(4,1,6)(0,0,0)[0] : AIC=36127.976, Time=7.85 sec ARIMA(5,1,7)(0,0,0)[0] : AIC=36093.608, Time=11.12 sec ARIMA(4,1,7)(0,0,0)[0] : AIC=inf, Time=9.16 sec ARIMA(5,1,6)(0,0,0)[0] intercept : AIC=36089.114, Time=14.21 sec Best model: ARIMA(5,1,6)(0,0,0)[0] Total fit time: 591.682 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=34346.447, Time=0.18 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=33361.909, Time=0.29 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=32491.971, Time=0.58 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=34344.447, Time=0.04 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=32493.360, Time=1.22 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=32493.403, Time=1.08 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=32495.966, Time=1.18 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=32490.031, Time=0.34 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=32491.422, Time=0.59 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=32491.465, Time=0.51 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=33359.910, Time=0.17 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=32494.026, Time=0.65 sec Best model: ARIMA(0,1,1)(0,0,0)[0] Total fit time: 6.854 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=33919.824, Time=0.13 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=33032.486, Time=0.29 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=31899.189, Time=0.68 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=33917.824, Time=0.08 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=31901.058, Time=1.36 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=31901.048, Time=1.08 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=31902.827, Time=3.14 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=31897.189, Time=0.33 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=31899.058, Time=0.55 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=31899.048, Time=0.54 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=33030.486, Time=0.17 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=31900.827, Time=1.50 sec Best model: ARIMA(0,1,1)(0,0,0)[0] Total fit time: 9.853 seconds
c:\users\pgsva\miniconda3\lib\site-packages\pmdarima\arima\auto.py:444: UserWarning: Input time-series is completely constant; returning a (0, 0, 0) ARMA.
warnings.warn('Input time-series is completely constant; '
ARIMA(0,0,0)(0,0,0)[0] : AIC=-72354.931, Time=0.37 sec Total fit time: 0.383 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=34695.447, Time=0.16 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=34461.635, Time=0.31 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=33738.856, Time=0.75 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=34693.448, Time=0.07 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=33439.533, Time=1.53 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=33377.732, Time=2.30 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=34323.820, Time=0.37 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=33257.081, Time=2.58 sec ARIMA(3,1,0)(0,0,0)[0] intercept : AIC=34144.636, Time=0.50 sec ARIMA(4,1,1)(0,0,0)[0] intercept : AIC=33124.355, Time=3.69 sec ARIMA(4,1,0)(0,0,0)[0] intercept : AIC=33903.724, Time=0.76 sec ARIMA(5,1,1)(0,0,0)[0] intercept : AIC=32845.459, Time=5.19 sec ARIMA(5,1,0)(0,0,0)[0] intercept : AIC=33253.538, Time=1.03 sec ARIMA(6,1,1)(0,0,0)[0] intercept : AIC=32595.793, Time=6.83 sec ARIMA(6,1,0)(0,0,0)[0] intercept : AIC=32594.195, Time=1.80 sec ARIMA(7,1,0)(0,0,0)[0] intercept : AIC=32595.606, Time=3.91 sec ARIMA(7,1,1)(0,0,0)[0] intercept : AIC=32595.810, Time=7.93 sec ARIMA(6,1,0)(0,0,0)[0] : AIC=32592.213, Time=0.92 sec ARIMA(5,1,0)(0,0,0)[0] : AIC=33251.546, Time=0.57 sec ARIMA(7,1,0)(0,0,0)[0] : AIC=32593.624, Time=1.87 sec ARIMA(6,1,1)(0,0,0)[0] : AIC=32593.811, Time=3.54 sec ARIMA(5,1,1)(0,0,0)[0] : AIC=32843.477, Time=1.99 sec ARIMA(7,1,1)(0,0,0)[0] : AIC=32593.828, Time=3.36 sec Best model: ARIMA(6,1,0)(0,0,0)[0] Total fit time: 52.002 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=37001.358, Time=0.14 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=36617.960, Time=0.25 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=35738.932, Time=0.86 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=36999.362, Time=0.08 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=35602.404, Time=1.49 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=35565.158, Time=1.64 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=36392.625, Time=0.43 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=35508.874, Time=3.13 sec ARIMA(3,1,0)(0,0,0)[0] intercept : AIC=36226.199, Time=0.53 sec ARIMA(4,1,1)(0,0,0)[0] intercept : AIC=35409.081, Time=4.21 sec ARIMA(4,1,0)(0,0,0)[0] intercept : AIC=36059.879, Time=0.77 sec ARIMA(5,1,1)(0,0,0)[0] intercept : AIC=35147.057, Time=5.37 sec ARIMA(5,1,0)(0,0,0)[0] intercept : AIC=35546.157, Time=1.06 sec ARIMA(6,1,1)(0,0,0)[0] intercept : AIC=34925.946, Time=7.26 sec ARIMA(6,1,0)(0,0,0)[0] intercept : AIC=34934.692, Time=1.58 sec ARIMA(7,1,1)(0,0,0)[0] intercept : AIC=34919.316, Time=11.07 sec ARIMA(7,1,0)(0,0,0)[0] intercept : AIC=34920.734, Time=1.98 sec ARIMA(8,1,1)(0,0,0)[0] intercept : AIC=34891.679, Time=7.67 sec ARIMA(8,1,0)(0,0,0)[0] intercept : AIC=34893.066, Time=2.70 sec ARIMA(9,1,1)(0,0,0)[0] intercept : AIC=34868.841, Time=17.08 sec ARIMA(9,1,0)(0,0,0)[0] intercept : AIC=34893.585, Time=2.93 sec ARIMA(10,1,1)(0,0,0)[0] intercept : AIC=34861.298, Time=17.68 sec ARIMA(10,1,0)(0,0,0)[0] intercept : AIC=34889.939, Time=3.91 sec ARIMA(10,1,2)(0,0,0)[0] intercept : AIC=34844.542, Time=22.53 sec ARIMA(9,1,2)(0,0,0)[0] intercept : AIC=34837.992, Time=20.76 sec ARIMA(8,1,2)(0,0,0)[0] intercept : AIC=34895.576, Time=15.38 sec ARIMA(9,1,3)(0,0,0)[0] intercept : AIC=34732.898, Time=22.98 sec ARIMA(8,1,3)(0,0,0)[0] intercept : AIC=34879.929, Time=16.79 sec ARIMA(10,1,3)(0,0,0)[0] intercept : AIC=34839.615, Time=23.52 sec ARIMA(9,1,4)(0,0,0)[0] intercept : AIC=34755.601, Time=21.43 sec ARIMA(8,1,4)(0,0,0)[0] intercept : AIC=34879.608, Time=16.50 sec ARIMA(10,1,4)(0,0,0)[0] intercept : AIC=34777.824, Time=28.20 sec ARIMA(9,1,3)(0,0,0)[0] : AIC=34794.968, Time=9.36 sec Best model: ARIMA(9,1,3)(0,0,0)[0] intercept Total fit time: 291.312 seconds
In [64]:
plotARIMAfunc(train_df_PA, test_df_PA, fit_df_PA, forecast_df_PA, lower_df_PA, upper_df_PA)
RMSE for BRYANT Stations: 54.02127600872799 RMSE for CAMBRIDGE Stations: 64.20669476951068 RMSE for HAMILTON Stations: 6.267958501138296 RMSE for HIGH Stations: 41.74034056235554 RMSE for MPL Stations: 24.221816397569082 RMSE for RINCONADA LIB Stations: 1.3576936502378508e-05 RMSE for SHERMAN Stations: 26.62721201578065 RMSE for TED THOMPSON Stations: 30.182614413955648 RMSE for WEBSTER Stations: 43.15314186731695
Dundee¶
In [65]:
data_dundee = pd.read_csv('data/Dundee_merged.csv')
C:\Users\pgsva\AppData\Local\Temp\ipykernel_15248\1761076983.py:1: DtypeWarning: Columns (1) have mixed types. Specify dtype option on import or set low_memory=False.
data_dundee = pd.read_csv('data/Dundee_merged.csv')
In [66]:
data_dundee = data_dundee.assign(timestamp=pd.to_datetime(data_dundee["End Date"]).dt.date)
data_dundee = data_dundee[["timestamp", "Address 1", "Energy(kWh)"]].groupby(["timestamp", "Address 1"], as_index=False).sum()
data_dundee = pd.pivot_table(data_dundee, values="Energy(kWh)", index="timestamp", columns= "Address 1", aggfunc=np.sum, fill_value=0)
data_dundee.reset_index(inplace=True)
In [67]:
data_dundee.head(10)
Out[67]:
| Address 1 | timestamp | ***TEST SITE*** Charge Your Car HQ | Ardler Complex, Dundee | Balunie Drive, Dundee | Brington Place Sheltered Housing, Dundee | DCC Environment, 34 Harefield Road | Dock Street, Dundee | Dundee House, Dundee | Dundee Ice Arena, Dundee | Earn Cresent, Dundee | ... | Sinclair Street | Sinclair Street, Dundee | Social Work Building, Jack Martin Way, Dundee | South Tay Street | South Tay Street, Dundee | Trades Lane | Trades Lane, Dundee | Turriff House Rannoch Road, Dundee | University of Dundee, Nethergate, Dundee | Whitfield Centre, Dundee |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1970-01-01 | 0.0 | 0.00 | 0.00 | 0.00 | 0.00 | 0.000 | 0.00 | 0.000 | 0.00 | ... | 0.000 | 0.0 | 0.000 | 0.000 | 0.0 | 0.000 | 0.0 | 0.00 | 0.0 | 0.00 |
| 1 | 2017-09-01 | 0.0 | 0.00 | 2.08 | 14.06 | 1.36 | 7.623 | 5.72 | 245.582 | 0.00 | ... | 2.551 | 0.0 | 70.930 | 19.517 | 0.0 | 3.804 | 0.0 | 0.00 | 0.0 | 23.61 |
| 2 | 2017-09-02 | 0.0 | 0.00 | 47.17 | 7.69 | 11.17 | 36.744 | 0.00 | 340.500 | 15.13 | ... | 20.024 | 0.0 | 16.130 | 14.021 | 0.0 | 4.558 | 0.0 | 9.92 | 0.0 | 7.02 |
| 3 | 2017-09-03 | 0.0 | 0.00 | 30.94 | -10.46 | 0.00 | 9.593 | 0.00 | 269.280 | 0.00 | ... | 21.638 | 0.0 | 0.000 | 24.964 | 0.0 | 10.384 | 0.0 | 0.00 | 0.0 | 0.00 |
| 4 | 2017-09-04 | 0.0 | 0.00 | 23.19 | 18.50 | 20.75 | 16.714 | 13.98 | 186.840 | 0.00 | ... | 13.448 | 0.0 | 41.036 | 8.362 | 0.0 | 13.136 | 0.0 | 0.00 | 0.0 | 17.08 |
| 5 | 2017-09-05 | 0.0 | 0.00 | 22.27 | 12.44 | 4.03 | 17.464 | 24.21 | 221.061 | 0.00 | ... | 0.563 | 0.0 | 37.220 | 26.702 | 0.0 | 0.000 | 0.0 | 0.00 | 0.0 | 22.65 |
| 6 | 2017-09-06 | 0.0 | 0.00 | 47.46 | 11.67 | 12.08 | 15.542 | 37.35 | 295.905 | 10.96 | ... | 7.973 | 0.0 | 15.410 | 17.055 | 0.0 | 1.800 | 0.0 | 10.15 | 0.0 | 39.93 |
| 7 | 2017-09-07 | 0.0 | 0.00 | 0.00 | 19.10 | 0.00 | 19.081 | 34.98 | 297.950 | 9.54 | ... | 18.134 | 0.0 | 9.800 | 47.267 | 0.0 | 11.660 | 0.0 | 0.00 | 0.0 | 18.52 |
| 8 | 2017-09-08 | 0.0 | 7.21 | 26.97 | 8.42 | 11.81 | 16.365 | 28.42 | 330.680 | 45.88 | ... | 17.007 | 0.0 | 45.470 | 0.000 | 0.0 | 16.669 | 0.0 | 25.55 | 0.0 | 15.32 |
| 9 | 2017-09-09 | 0.0 | 0.00 | 25.24 | 9.46 | 15.33 | 5.485 | 0.00 | 319.501 | 10.12 | ... | 0.000 | 0.0 | 20.900 | 41.381 | 0.0 | 8.049 | 0.0 | 0.00 | 0.0 | 13.00 |
10 rows × 35 columns
In [68]:
print(data_dundee[data_dundee == 0].count(axis=0)/len(data_dundee.index))
Address 1 timestamp 0.000000 ***TEST SITE*** Charge Your Car HQ 0.965241 Ardler Complex, Dundee 0.780749 Balunie Drive, Dundee 0.259358 Brington Place Sheltered Housing, Dundee 0.042781 DCC Environment, 34 Harefield Road 0.655080 Dock Street, Dundee 0.050802 Dundee House, Dundee 0.296791 Dundee Ice Arena, Dundee 0.093583 Earn Cresent, Dundee 0.748663 Gellatly Street Car Park, Dundee 0.008021 Greenmarket Multi Car Park, Dundee 0.010695 Housing Office East, Dundee 0.165775 Housing Office West, Dundee 0.165775 Janet Brougham House, Dundee 0.427807 Lochee Charging Hub, Dundee 0.596257 Marchbanks, Dundee 0.216578 Menziehill House, Dundee 0.195187 Mitchell Street, Dundee 0.687166 Nethergate, Dundee 0.125668 Oakland Day Centre, Dundee 0.500000 Olympia Multi-Storey Car Park, Dundee 0.048128 Princes Street Charging Hub 0.863636 Public Works Dept, Clepington Rd. Dundee 0.016043 Queen Street Car Park, Broughty Ferry, Dundee 0.008021 Sinclair Street 0.590909 Sinclair Street, Dundee 0.967914 Social Work Building, Jack Martin Way, Dundee 0.048128 South Tay Street 0.566845 South Tay Street, Dundee 0.459893 Trades Lane 0.580214 Trades Lane, Dundee 0.641711 Turriff House Rannoch Road, Dundee 0.676471 University of Dundee, Nethergate, Dundee 0.556150 Whitfield Centre, Dundee 0.109626 dtype: float64
In [69]:
train_df_dundee, test_df_dundee, fit_df_dundee, forecast_df_dundee, lower_df_dundee, upper_df_dundee = autoARIMAfunc(data_dundee)
Performing stepwise search to minimize aic ARIMA(0,0,0)(0,0,0)[0] intercept : AIC=4037.793, Time=0.03 sec ARIMA(1,0,0)(0,0,0)[0] intercept : AIC=3628.415, Time=0.10 sec ARIMA(0,0,1)(0,0,0)[0] intercept : AIC=3769.824, Time=0.20 sec ARIMA(0,0,0)(0,0,0)[0] : AIC=4044.992, Time=0.01 sec ARIMA(2,0,0)(0,0,0)[0] intercept : AIC=3525.384, Time=0.16 sec ARIMA(3,0,0)(0,0,0)[0] intercept : AIC=3525.115, Time=0.26 sec ARIMA(4,0,0)(0,0,0)[0] intercept : AIC=3493.546, Time=0.29 sec ARIMA(5,0,0)(0,0,0)[0] intercept : AIC=3482.337, Time=0.29 sec ARIMA(6,0,0)(0,0,0)[0] intercept : AIC=3484.088, Time=0.35 sec ARIMA(5,0,1)(0,0,0)[0] intercept : AIC=3484.143, Time=0.55 sec ARIMA(4,0,1)(0,0,0)[0] intercept : AIC=3484.971, Time=0.69 sec ARIMA(6,0,1)(0,0,0)[0] intercept : AIC=3485.823, Time=1.14 sec ARIMA(5,0,0)(0,0,0)[0] : AIC=3482.625, Time=0.21 sec Best model: ARIMA(5,0,0)(0,0,0)[0] intercept Total fit time: 4.318 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2278.628, Time=0.02 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2118.044, Time=0.08 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2040.095, Time=0.20 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2276.628, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2022.132, Time=0.14 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=2022.969, Time=0.19 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=2023.256, Time=0.21 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=2021.624, Time=0.16 sec ARIMA(0,1,3)(0,0,0)[0] intercept : AIC=2023.144, Time=0.18 sec ARIMA(1,1,3)(0,0,0)[0] intercept : AIC=2025.060, Time=0.47 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=2019.639, Time=0.08 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=2038.108, Time=0.06 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=2021.271, Time=0.13 sec ARIMA(0,1,3)(0,0,0)[0] : AIC=2021.159, Time=0.11 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=2020.147, Time=0.07 sec ARIMA(1,1,3)(0,0,0)[0] : AIC=2023.075, Time=0.30 sec Best model: ARIMA(0,1,2)(0,0,0)[0] Total fit time: 2.451 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=3142.392, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2987.076, Time=0.10 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2891.421, Time=0.13 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=3140.392, Time=0.03 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2884.857, Time=0.16 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=2885.662, Time=0.28 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=2882.518, Time=0.23 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=2886.045, Time=0.19 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=2883.839, Time=0.43 sec ARIMA(1,1,3)(0,0,0)[0] intercept : AIC=2883.826, Time=0.44 sec ARIMA(0,1,3)(0,0,0)[0] intercept : AIC=2886.004, Time=0.30 sec ARIMA(2,1,3)(0,0,0)[0] intercept : AIC=2885.826, Time=0.74 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=2880.684, Time=0.18 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=2884.188, Time=0.10 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=2882.997, Time=0.10 sec ARIMA(2,1,2)(0,0,0)[0] : AIC=2881.989, Time=0.28 sec ARIMA(1,1,3)(0,0,0)[0] : AIC=2881.975, Time=0.33 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=2889.631, Time=0.05 sec ARIMA(0,1,3)(0,0,0)[0] : AIC=2884.168, Time=0.18 sec ARIMA(2,1,1)(0,0,0)[0] : AIC=2883.824, Time=0.19 sec ARIMA(2,1,3)(0,0,0)[0] : AIC=2883.974, Time=0.47 sec Best model: ARIMA(1,1,2)(0,0,0)[0] Total fit time: 4.936 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2596.225, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2546.615, Time=0.17 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2429.353, Time=0.15 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2594.228, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2426.455, Time=0.20 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=2424.042, Time=0.34 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=2514.787, Time=0.18 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=2423.586, Time=0.28 sec ARIMA(3,1,0)(0,0,0)[0] intercept : AIC=2484.064, Time=0.27 sec ARIMA(4,1,1)(0,0,0)[0] intercept : AIC=2425.579, Time=0.44 sec ARIMA(3,1,2)(0,0,0)[0] intercept : AIC=2425.580, Time=0.54 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=2424.261, Time=0.54 sec ARIMA(4,1,0)(0,0,0)[0] intercept : AIC=2468.021, Time=0.35 sec ARIMA(4,1,2)(0,0,0)[0] intercept : AIC=2423.870, Time=0.64 sec ARIMA(3,1,1)(0,0,0)[0] : AIC=2421.595, Time=0.21 sec ARIMA(2,1,1)(0,0,0)[0] : AIC=2422.056, Time=0.21 sec ARIMA(3,1,0)(0,0,0)[0] : AIC=2482.082, Time=0.10 sec ARIMA(4,1,1)(0,0,0)[0] : AIC=2423.589, Time=0.26 sec ARIMA(3,1,2)(0,0,0)[0] : AIC=2423.589, Time=0.37 sec ARIMA(2,1,0)(0,0,0)[0] : AIC=2512.793, Time=0.07 sec ARIMA(2,1,2)(0,0,0)[0] : AIC=2422.271, Time=0.32 sec ARIMA(4,1,0)(0,0,0)[0] : AIC=2466.043, Time=0.15 sec ARIMA(4,1,2)(0,0,0)[0] : AIC=2421.880, Time=0.47 sec Best model: ARIMA(3,1,1)(0,0,0)[0] Total fit time: 6.319 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2828.710, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2789.673, Time=0.13 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2678.998, Time=0.13 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2826.710, Time=0.03 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2671.739, Time=0.23 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=2667.264, Time=0.26 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=2749.277, Time=0.17 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=2668.922, Time=0.35 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=2670.643, Time=0.40 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=2668.667, Time=0.25 sec ARIMA(3,1,0)(0,0,0)[0] intercept : AIC=2732.319, Time=0.15 sec ARIMA(3,1,2)(0,0,0)[0] intercept : AIC=inf, Time=0.87 sec ARIMA(2,1,1)(0,0,0)[0] : AIC=2665.519, Time=0.20 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=2670.154, Time=0.14 sec ARIMA(2,1,0)(0,0,0)[0] : AIC=2747.277, Time=0.08 sec ARIMA(3,1,1)(0,0,0)[0] : AIC=2667.140, Time=0.26 sec ARIMA(2,1,2)(0,0,0)[0] : AIC=2669.009, Time=0.26 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=2787.673, Time=0.07 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=2667.017, Time=0.19 sec ARIMA(3,1,0)(0,0,0)[0] : AIC=2730.320, Time=0.11 sec ARIMA(3,1,2)(0,0,0)[0] : AIC=inf, Time=0.80 sec Best model: ARIMA(2,1,1)(0,0,0)[0] Total fit time: 5.120 seconds Performing stepwise search to minimize aic ARIMA(0,0,0)(0,0,0)[0] intercept : AIC=2679.051, Time=0.03 sec ARIMA(1,0,0)(0,0,0)[0] intercept : AIC=2679.538, Time=0.16 sec ARIMA(0,0,1)(0,0,0)[0] intercept : AIC=2679.620, Time=0.11 sec ARIMA(0,0,0)(0,0,0)[0] : AIC=3073.058, Time=0.02 sec ARIMA(1,0,1)(0,0,0)[0] intercept : AIC=2674.738, Time=0.50 sec ARIMA(2,0,1)(0,0,0)[0] intercept : AIC=2676.472, Time=0.65 sec ARIMA(1,0,2)(0,0,0)[0] intercept : AIC=2676.419, Time=0.69 sec ARIMA(0,0,2)(0,0,0)[0] intercept : AIC=2681.420, Time=0.22 sec ARIMA(2,0,0)(0,0,0)[0] intercept : AIC=2681.184, Time=0.19 sec ARIMA(2,0,2)(0,0,0)[0] intercept : AIC=inf, Time=0.87 sec ARIMA(1,0,1)(0,0,0)[0] : AIC=2685.128, Time=0.15 sec Best model: ARIMA(1,0,1)(0,0,0)[0] intercept Total fit time: 3.597 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=3430.000, Time=0.02 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=3419.446, Time=0.05 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=3333.340, Time=0.16 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=3428.001, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=inf, Time=0.31 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=3290.815, Time=0.26 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=3292.769, Time=0.38 sec ARIMA(0,1,3)(0,0,0)[0] intercept : AIC=3292.703, Time=0.32 sec ARIMA(1,1,3)(0,0,0)[0] intercept : AIC=3283.561, Time=0.52 sec ARIMA(2,1,3)(0,0,0)[0] intercept : AIC=inf, Time=1.14 sec ARIMA(1,1,4)(0,0,0)[0] intercept : AIC=3273.465, Time=0.61 sec ARIMA(0,1,4)(0,0,0)[0] intercept : AIC=3273.494, Time=0.41 sec ARIMA(2,1,4)(0,0,0)[0] intercept : AIC=inf, Time=1.36 sec ARIMA(1,1,5)(0,0,0)[0] intercept : AIC=3269.410, Time=1.05 sec ARIMA(0,1,5)(0,0,0)[0] intercept : AIC=3273.751, Time=0.67 sec ARIMA(2,1,5)(0,0,0)[0] intercept : AIC=inf, Time=1.59 sec ARIMA(1,1,6)(0,0,0)[0] intercept : AIC=3271.147, Time=1.00 sec ARIMA(0,1,6)(0,0,0)[0] intercept : AIC=3272.215, Time=0.85 sec ARIMA(2,1,6)(0,0,0)[0] intercept : AIC=inf, Time=1.70 sec ARIMA(1,1,5)(0,0,0)[0] : AIC=3267.453, Time=0.72 sec ARIMA(0,1,5)(0,0,0)[0] : AIC=3271.792, Time=0.45 sec ARIMA(1,1,4)(0,0,0)[0] : AIC=3271.506, Time=0.41 sec ARIMA(2,1,5)(0,0,0)[0] : AIC=inf, Time=1.35 sec ARIMA(1,1,6)(0,0,0)[0] : AIC=3269.189, Time=0.67 sec ARIMA(0,1,4)(0,0,0)[0] : AIC=3271.535, Time=0.25 sec ARIMA(0,1,6)(0,0,0)[0] : AIC=3270.253, Time=0.47 sec ARIMA(2,1,4)(0,0,0)[0] : AIC=inf, Time=1.00 sec ARIMA(2,1,6)(0,0,0)[0] : AIC=inf, Time=1.28 sec Best model: ARIMA(1,1,5)(0,0,0)[0] Total fit time: 19.083 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=3829.864, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=3806.334, Time=0.20 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=3766.022, Time=0.10 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=3827.869, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=3737.429, Time=0.24 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=3737.908, Time=0.45 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=3738.459, Time=0.29 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=3738.706, Time=0.19 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=3794.029, Time=0.28 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=3740.640, Time=0.60 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=3737.542, Time=0.18 sec Best model: ARIMA(1,1,1)(0,0,0)[0] intercept Total fit time: 2.594 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2624.904, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2547.137, Time=0.10 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2448.578, Time=0.12 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2622.904, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2448.443, Time=0.20 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=2450.432, Time=0.25 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=2444.025, Time=0.22 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=2448.470, Time=0.18 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=2445.526, Time=0.28 sec ARIMA(1,1,3)(0,0,0)[0] intercept : AIC=2445.577, Time=0.50 sec ARIMA(0,1,3)(0,0,0)[0] intercept : AIC=2450.460, Time=0.33 sec ARIMA(2,1,3)(0,0,0)[0] intercept : AIC=inf, Time=1.05 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=2442.245, Time=0.17 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=2446.728, Time=0.10 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=2446.709, Time=0.09 sec ARIMA(2,1,2)(0,0,0)[0] : AIC=2443.784, Time=0.22 sec ARIMA(1,1,3)(0,0,0)[0] : AIC=2443.830, Time=0.37 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=2446.763, Time=0.06 sec ARIMA(0,1,3)(0,0,0)[0] : AIC=2448.723, Time=0.12 sec ARIMA(2,1,1)(0,0,0)[0] : AIC=2448.703, Time=0.15 sec ARIMA(2,1,3)(0,0,0)[0] : AIC=2444.812, Time=0.52 sec Best model: ARIMA(1,1,2)(0,0,0)[0] Total fit time: 5.094 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=3440.544, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=3388.836, Time=0.13 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=3268.490, Time=0.16 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=3438.554, Time=0.03 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=3265.996, Time=0.24 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=3263.760, Time=0.33 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=3328.210, Time=0.21 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=3263.456, Time=0.47 sec ARIMA(3,1,0)(0,0,0)[0] intercept : AIC=3325.104, Time=0.23 sec ARIMA(4,1,1)(0,0,0)[0] intercept : AIC=3258.003, Time=0.54 sec ARIMA(4,1,0)(0,0,0)[0] intercept : AIC=3322.442, Time=0.30 sec ARIMA(5,1,1)(0,0,0)[0] intercept : AIC=3239.231, Time=0.58 sec ARIMA(5,1,0)(0,0,0)[0] intercept : AIC=3273.941, Time=0.39 sec ARIMA(6,1,1)(0,0,0)[0] intercept : AIC=3236.600, Time=1.51 sec ARIMA(6,1,0)(0,0,0)[0] intercept : AIC=3237.425, Time=0.54 sec ARIMA(7,1,1)(0,0,0)[0] intercept : AIC=3228.405, Time=0.98 sec ARIMA(7,1,0)(0,0,0)[0] intercept : AIC=3235.764, Time=0.53 sec ARIMA(8,1,1)(0,0,0)[0] intercept : AIC=3229.880, Time=1.21 sec ARIMA(7,1,2)(0,0,0)[0] intercept : AIC=3230.159, Time=1.36 sec ARIMA(6,1,2)(0,0,0)[0] intercept : AIC=3238.272, Time=1.07 sec ARIMA(8,1,0)(0,0,0)[0] intercept : AIC=3236.601, Time=0.94 sec ARIMA(8,1,2)(0,0,0)[0] intercept : AIC=3230.207, Time=1.52 sec ARIMA(7,1,1)(0,0,0)[0] : AIC=3226.894, Time=0.68 sec ARIMA(6,1,1)(0,0,0)[0] : AIC=3234.779, Time=0.81 sec ARIMA(7,1,0)(0,0,0)[0] : AIC=3233.943, Time=0.19 sec ARIMA(8,1,1)(0,0,0)[0] : AIC=3228.357, Time=0.81 sec ARIMA(7,1,2)(0,0,0)[0] : AIC=3228.641, Time=0.95 sec ARIMA(6,1,0)(0,0,0)[0] : AIC=3235.583, Time=0.29 sec ARIMA(6,1,2)(0,0,0)[0] : AIC=3236.440, Time=0.77 sec ARIMA(8,1,0)(0,0,0)[0] : AIC=3234.772, Time=0.39 sec ARIMA(8,1,2)(0,0,0)[0] : AIC=3228.686, Time=0.89 sec Best model: ARIMA(7,1,1)(0,0,0)[0] Total fit time: 19.082 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=3869.158, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=3826.068, Time=0.08 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=3799.768, Time=0.19 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=3867.161, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=3789.585, Time=0.24 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=3789.912, Time=0.30 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=3789.766, Time=0.36 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=3792.874, Time=0.26 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=3813.317, Time=0.18 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=3791.764, Time=0.63 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=3787.592, Time=0.12 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=3797.785, Time=0.08 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=3824.075, Time=0.04 sec ARIMA(2,1,1)(0,0,0)[0] : AIC=3787.914, Time=0.21 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=3787.767, Time=0.23 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=3790.887, Time=0.12 sec ARIMA(2,1,0)(0,0,0)[0] : AIC=3811.328, Time=0.11 sec ARIMA(2,1,2)(0,0,0)[0] : AIC=3789.766, Time=0.43 sec Best model: ARIMA(1,1,1)(0,0,0)[0] Total fit time: 3.643 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2995.221, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2956.519, Time=0.09 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2850.400, Time=0.11 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2993.243, Time=0.03 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2841.579, Time=0.24 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=2838.389, Time=0.31 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=2921.802, Time=0.15 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=2839.670, Time=0.34 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=2837.294, Time=0.58 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=2840.097, Time=0.29 sec ARIMA(3,1,2)(0,0,0)[0] intercept : AIC=2839.158, Time=0.87 sec ARIMA(2,1,3)(0,0,0)[0] intercept : AIC=2843.112, Time=0.50 sec ARIMA(1,1,3)(0,0,0)[0] intercept : AIC=2838.551, Time=0.46 sec ARIMA(3,1,3)(0,0,0)[0] intercept : AIC=2841.268, Time=0.61 sec ARIMA(2,1,2)(0,0,0)[0] : AIC=2836.114, Time=0.33 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=2839.102, Time=0.20 sec ARIMA(2,1,1)(0,0,0)[0] : AIC=2837.364, Time=0.19 sec ARIMA(3,1,2)(0,0,0)[0] : AIC=2837.968, Time=0.66 sec ARIMA(2,1,3)(0,0,0)[0] : AIC=2800.499, Time=0.86 sec ARIMA(1,1,3)(0,0,0)[0] : AIC=2837.396, Time=0.23 sec ARIMA(3,1,3)(0,0,0)[0] : AIC=2840.089, Time=0.39 sec ARIMA(2,1,4)(0,0,0)[0] : AIC=2798.255, Time=1.05 sec ARIMA(1,1,4)(0,0,0)[0] : AIC=2838.882, Time=0.45 sec ARIMA(3,1,4)(0,0,0)[0] : AIC=2800.046, Time=1.11 sec ARIMA(2,1,5)(0,0,0)[0] : AIC=2798.697, Time=1.11 sec ARIMA(1,1,5)(0,0,0)[0] : AIC=2841.693, Time=0.50 sec ARIMA(3,1,5)(0,0,0)[0] : AIC=2800.022, Time=1.17 sec ARIMA(2,1,4)(0,0,0)[0] intercept : AIC=2826.225, Time=1.38 sec Best model: ARIMA(2,1,4)(0,0,0)[0] Total fit time: 14.256 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2838.446, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2737.233, Time=0.12 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2622.442, Time=0.13 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2836.452, Time=0.03 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2624.403, Time=0.22 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=2624.404, Time=0.21 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=inf, Time=0.64 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=2620.461, Time=0.07 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=2622.420, Time=0.12 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=2622.421, Time=0.12 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=2735.241, Time=0.05 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=inf, Time=0.43 sec Best model: ARIMA(0,1,1)(0,0,0)[0] Total fit time: 2.182 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2335.577, Time=0.02 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2261.849, Time=0.11 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2229.368, Time=0.11 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2333.577, Time=0.03 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2231.014, Time=0.16 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=2231.087, Time=0.16 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=2228.849, Time=0.53 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=2230.353, Time=0.48 sec ARIMA(1,1,3)(0,0,0)[0] intercept : AIC=2230.249, Time=0.43 sec ARIMA(0,1,3)(0,0,0)[0] intercept : AIC=2232.208, Time=0.21 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=2230.660, Time=0.28 sec ARIMA(2,1,3)(0,0,0)[0] intercept : AIC=2231.997, Time=0.73 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=2227.257, Time=0.35 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=2229.170, Time=0.08 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=2229.104, Time=0.07 sec ARIMA(2,1,2)(0,0,0)[0] : AIC=2228.760, Time=0.31 sec ARIMA(1,1,3)(0,0,0)[0] : AIC=2228.656, Time=0.24 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=2227.435, Time=0.06 sec ARIMA(0,1,3)(0,0,0)[0] : AIC=2230.331, Time=0.12 sec ARIMA(2,1,1)(0,0,0)[0] : AIC=2228.917, Time=0.15 sec ARIMA(2,1,3)(0,0,0)[0] : AIC=2230.403, Time=0.35 sec Best model: ARIMA(1,1,2)(0,0,0)[0] Total fit time: 4.991 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=4249.011, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=4238.424, Time=0.06 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=4233.620, Time=0.17 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=4247.094, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=4205.804, Time=0.29 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=4205.993, Time=0.43 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=4206.924, Time=0.40 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=4213.342, Time=0.18 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=4238.396, Time=0.08 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=4182.583, Time=0.75 sec ARIMA(3,1,2)(0,0,0)[0] intercept : AIC=4138.690, Time=0.90 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=4187.240, Time=0.56 sec ARIMA(4,1,2)(0,0,0)[0] intercept : AIC=4131.721, Time=1.25 sec ARIMA(4,1,1)(0,0,0)[0] intercept : AIC=4184.449, Time=0.75 sec ARIMA(5,1,2)(0,0,0)[0] intercept : AIC=4126.813, Time=1.32 sec ARIMA(5,1,1)(0,0,0)[0] intercept : AIC=4171.104, Time=0.53 sec ARIMA(6,1,2)(0,0,0)[0] intercept : AIC=4132.682, Time=1.32 sec ARIMA(5,1,3)(0,0,0)[0] intercept : AIC=4125.629, Time=1.34 sec ARIMA(4,1,3)(0,0,0)[0] intercept : AIC=inf, Time=1.20 sec ARIMA(6,1,3)(0,0,0)[0] intercept : AIC=4133.743, Time=1.54 sec ARIMA(5,1,4)(0,0,0)[0] intercept : AIC=4101.288, Time=1.46 sec ARIMA(4,1,4)(0,0,0)[0] intercept : AIC=4131.353, Time=1.30 sec ARIMA(6,1,4)(0,0,0)[0] intercept : AIC=4101.097, Time=1.69 sec ARIMA(7,1,4)(0,0,0)[0] intercept : AIC=4103.724, Time=1.81 sec ARIMA(6,1,5)(0,0,0)[0] intercept : AIC=4103.301, Time=1.86 sec ARIMA(5,1,5)(0,0,0)[0] intercept : AIC=4102.318, Time=1.81 sec ARIMA(7,1,3)(0,0,0)[0] intercept : AIC=4123.176, Time=1.66 sec ARIMA(7,1,5)(0,0,0)[0] intercept : AIC=4106.536, Time=1.99 sec ARIMA(6,1,4)(0,0,0)[0] : AIC=4099.681, Time=1.36 sec ARIMA(5,1,4)(0,0,0)[0] : AIC=4099.874, Time=1.28 sec ARIMA(6,1,3)(0,0,0)[0] : AIC=4132.512, Time=0.98 sec ARIMA(7,1,4)(0,0,0)[0] : AIC=4102.524, Time=1.68 sec ARIMA(6,1,5)(0,0,0)[0] : AIC=4101.635, Time=1.59 sec ARIMA(5,1,3)(0,0,0)[0] : AIC=4124.291, Time=0.95 sec ARIMA(5,1,5)(0,0,0)[0] : AIC=4100.845, Time=1.49 sec ARIMA(7,1,3)(0,0,0)[0] : AIC=4121.692, Time=1.24 sec ARIMA(7,1,5)(0,0,0)[0] : AIC=4107.047, Time=1.86 sec Best model: ARIMA(6,1,4)(0,0,0)[0] Total fit time: 39.186 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=3266.344, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=3223.970, Time=0.11 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=inf, Time=0.27 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=3264.347, Time=0.02 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=3186.077, Time=0.13 sec ARIMA(3,1,0)(0,0,0)[0] intercept : AIC=3177.518, Time=0.29 sec ARIMA(4,1,0)(0,0,0)[0] intercept : AIC=3164.954, Time=0.39 sec ARIMA(5,1,0)(0,0,0)[0] intercept : AIC=3108.323, Time=0.43 sec ARIMA(6,1,0)(0,0,0)[0] intercept : AIC=3029.576, Time=0.42 sec ARIMA(7,1,0)(0,0,0)[0] intercept : AIC=3023.320, Time=0.83 sec ARIMA(8,1,0)(0,0,0)[0] intercept : AIC=3024.715, Time=0.67 sec ARIMA(7,1,1)(0,0,0)[0] intercept : AIC=inf, Time=1.40 sec ARIMA(6,1,1)(0,0,0)[0] intercept : AIC=3024.851, Time=0.93 sec ARIMA(8,1,1)(0,0,0)[0] intercept : AIC=inf, Time=1.81 sec ARIMA(7,1,0)(0,0,0)[0] : AIC=3021.329, Time=0.41 sec ARIMA(6,1,0)(0,0,0)[0] : AIC=3027.582, Time=0.27 sec ARIMA(8,1,0)(0,0,0)[0] : AIC=3022.722, Time=0.35 sec ARIMA(7,1,1)(0,0,0)[0] : AIC=3010.968, Time=0.87 sec ARIMA(6,1,1)(0,0,0)[0] : AIC=3022.860, Time=0.54 sec ARIMA(8,1,1)(0,0,0)[0] : AIC=3010.714, Time=1.15 sec ARIMA(9,1,1)(0,0,0)[0] : AIC=3008.223, Time=0.99 sec ARIMA(9,1,0)(0,0,0)[0] : AIC=3024.674, Time=0.49 sec ARIMA(10,1,1)(0,0,0)[0] : AIC=3008.277, Time=1.22 sec ARIMA(9,1,2)(0,0,0)[0] : AIC=3004.865, Time=1.43 sec ARIMA(8,1,2)(0,0,0)[0] : AIC=3015.003, Time=1.47 sec ARIMA(10,1,2)(0,0,0)[0] : AIC=3009.606, Time=1.93 sec ARIMA(9,1,3)(0,0,0)[0] : AIC=3007.631, Time=2.06 sec ARIMA(8,1,3)(0,0,0)[0] : AIC=3008.899, Time=2.01 sec ARIMA(10,1,3)(0,0,0)[0] : AIC=3012.007, Time=2.07 sec ARIMA(9,1,2)(0,0,0)[0] intercept : AIC=3007.536, Time=2.43 sec Best model: ARIMA(9,1,2)(0,0,0)[0] Total fit time: 27.449 seconds Performing stepwise search to minimize aic ARIMA(0,0,0)(0,0,0)[0] intercept : AIC=2567.893, Time=0.03 sec ARIMA(1,0,0)(0,0,0)[0] intercept : AIC=2554.270, Time=0.12 sec ARIMA(0,0,1)(0,0,0)[0] intercept : AIC=2558.710, Time=0.16 sec ARIMA(0,0,0)(0,0,0)[0] : AIC=2797.485, Time=0.02 sec ARIMA(2,0,0)(0,0,0)[0] intercept : AIC=2543.486, Time=0.17 sec ARIMA(3,0,0)(0,0,0)[0] intercept : AIC=2543.783, Time=0.27 sec ARIMA(2,0,1)(0,0,0)[0] intercept : AIC=2532.808, Time=0.42 sec ARIMA(1,0,1)(0,0,0)[0] intercept : AIC=2530.929, Time=0.32 sec ARIMA(1,0,2)(0,0,0)[0] intercept : AIC=2532.815, Time=0.42 sec ARIMA(0,0,2)(0,0,0)[0] intercept : AIC=2549.745, Time=0.24 sec ARIMA(2,0,2)(0,0,0)[0] intercept : AIC=2532.013, Time=0.54 sec ARIMA(1,0,1)(0,0,0)[0] : AIC=2537.320, Time=0.12 sec Best model: ARIMA(1,0,1)(0,0,0)[0] intercept Total fit time: 2.845 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2594.004, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2494.026, Time=0.09 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=inf, Time=0.34 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2592.004, Time=0.02 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=2446.125, Time=0.15 sec ARIMA(3,1,0)(0,0,0)[0] intercept : AIC=2423.051, Time=0.19 sec ARIMA(4,1,0)(0,0,0)[0] intercept : AIC=2411.875, Time=0.20 sec ARIMA(5,1,0)(0,0,0)[0] intercept : AIC=2388.959, Time=0.26 sec ARIMA(6,1,0)(0,0,0)[0] intercept : AIC=2351.219, Time=0.34 sec ARIMA(7,1,0)(0,0,0)[0] intercept : AIC=2342.297, Time=0.39 sec ARIMA(8,1,0)(0,0,0)[0] intercept : AIC=2338.133, Time=0.45 sec ARIMA(9,1,0)(0,0,0)[0] intercept : AIC=2339.890, Time=0.61 sec ARIMA(8,1,1)(0,0,0)[0] intercept : AIC=inf, Time=2.04 sec ARIMA(7,1,1)(0,0,0)[0] intercept : AIC=inf, Time=1.00 sec ARIMA(9,1,1)(0,0,0)[0] intercept : AIC=inf, Time=1.06 sec ARIMA(8,1,0)(0,0,0)[0] : AIC=2336.170, Time=0.16 sec ARIMA(7,1,0)(0,0,0)[0] : AIC=2340.327, Time=0.14 sec ARIMA(9,1,0)(0,0,0)[0] : AIC=2337.929, Time=0.18 sec ARIMA(8,1,1)(0,0,0)[0] : AIC=2326.231, Time=0.43 sec ARIMA(7,1,1)(0,0,0)[0] : AIC=2327.733, Time=0.40 sec ARIMA(9,1,1)(0,0,0)[0] : AIC=inf, Time=0.51 sec ARIMA(8,1,2)(0,0,0)[0] : AIC=2328.415, Time=0.75 sec ARIMA(7,1,2)(0,0,0)[0] : AIC=inf, Time=0.52 sec ARIMA(9,1,2)(0,0,0)[0] : AIC=inf, Time=0.75 sec Best model: ARIMA(8,1,1)(0,0,0)[0] Total fit time: 11.013 seconds Performing stepwise search to minimize aic ARIMA(0,0,0)(0,0,0)[0] intercept : AIC=2768.540, Time=0.01 sec ARIMA(1,0,0)(0,0,0)[0] intercept : AIC=2766.785, Time=0.06 sec ARIMA(0,0,1)(0,0,0)[0] intercept : AIC=2767.106, Time=0.07 sec ARIMA(0,0,0)(0,0,0)[0] : AIC=3074.569, Time=0.01 sec ARIMA(2,0,0)(0,0,0)[0] intercept : AIC=2767.688, Time=0.08 sec ARIMA(1,0,1)(0,0,0)[0] intercept : AIC=2764.818, Time=0.25 sec ARIMA(2,0,1)(0,0,0)[0] intercept : AIC=2766.808, Time=0.26 sec ARIMA(1,0,2)(0,0,0)[0] intercept : AIC=2766.806, Time=0.24 sec ARIMA(0,0,2)(0,0,0)[0] intercept : AIC=2768.594, Time=0.08 sec ARIMA(2,0,2)(0,0,0)[0] intercept : AIC=2767.778, Time=0.38 sec ARIMA(1,0,1)(0,0,0)[0] : AIC=2777.475, Time=0.09 sec Best model: ARIMA(1,0,1)(0,0,0)[0] intercept Total fit time: 1.515 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2857.321, Time=0.01 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2787.185, Time=0.04 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2714.781, Time=0.06 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2855.324, Time=0.01 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2708.049, Time=0.13 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=inf, Time=0.29 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=2709.544, Time=0.21 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=2709.546, Time=0.09 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=2777.898, Time=0.08 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=2709.621, Time=0.21 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=2706.218, Time=0.05 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=2712.870, Time=0.02 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=2785.188, Time=0.02 sec ARIMA(2,1,1)(0,0,0)[0] : AIC=2707.030, Time=0.18 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=2707.736, Time=0.10 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=2707.685, Time=0.04 sec ARIMA(2,1,0)(0,0,0)[0] : AIC=2775.904, Time=0.03 sec ARIMA(2,1,2)(0,0,0)[0] : AIC=2707.833, Time=0.12 sec Best model: ARIMA(1,1,1)(0,0,0)[0] Total fit time: 1.704 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=3170.979, Time=0.01 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=3128.186, Time=0.05 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=3046.571, Time=0.07 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=3168.982, Time=0.01 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=3032.753, Time=0.12 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=3033.979, Time=0.16 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=3034.386, Time=0.20 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=3032.922, Time=0.10 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=3114.632, Time=0.13 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=inf, Time=0.37 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=3030.753, Time=0.05 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=3044.574, Time=0.02 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=3126.191, Time=0.03 sec ARIMA(2,1,1)(0,0,0)[0] : AIC=3031.979, Time=0.09 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=3032.386, Time=0.10 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=3030.922, Time=0.05 sec ARIMA(2,1,0)(0,0,0)[0] : AIC=3112.639, Time=0.05 sec ARIMA(2,1,2)(0,0,0)[0] : AIC=inf, Time=0.31 sec Best model: ARIMA(1,1,1)(0,0,0)[0] Total fit time: 1.934 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=3695.851, Time=0.01 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=3694.372, Time=0.02 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=3692.813, Time=0.06 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=3694.404, Time=0.01 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=3681.456, Time=0.15 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=3678.468, Time=0.19 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=3689.757, Time=0.07 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=3674.957, Time=0.26 sec ARIMA(3,1,0)(0,0,0)[0] intercept : AIC=3682.790, Time=0.10 sec ARIMA(4,1,1)(0,0,0)[0] intercept : AIC=3667.113, Time=0.20 sec ARIMA(4,1,0)(0,0,0)[0] intercept : AIC=3665.379, Time=0.13 sec ARIMA(5,1,0)(0,0,0)[0] intercept : AIC=3667.153, Time=0.19 sec ARIMA(5,1,1)(0,0,0)[0] intercept : AIC=3669.105, Time=0.27 sec ARIMA(4,1,0)(0,0,0)[0] : AIC=3665.227, Time=0.08 sec ARIMA(3,1,0)(0,0,0)[0] : AIC=3681.919, Time=0.05 sec ARIMA(5,1,0)(0,0,0)[0] : AIC=3667.096, Time=0.10 sec ARIMA(4,1,1)(0,0,0)[0] : AIC=3667.067, Time=0.13 sec ARIMA(3,1,1)(0,0,0)[0] : AIC=3674.729, Time=0.11 sec ARIMA(5,1,1)(0,0,0)[0] : AIC=3669.064, Time=0.18 sec Best model: ARIMA(4,1,0)(0,0,0)[0] Total fit time: 2.316 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=3740.639, Time=0.01 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=3684.192, Time=0.08 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=3655.189, Time=0.07 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=3738.640, Time=0.01 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=3642.652, Time=0.15 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=inf, Time=0.25 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=3654.750, Time=0.18 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=3650.402, Time=0.14 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=3669.084, Time=0.11 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=3646.632, Time=0.23 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=3646.078, Time=0.07 sec Best model: ARIMA(1,1,1)(0,0,0)[0] intercept Total fit time: 1.314 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=3849.076, Time=0.01 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=3802.844, Time=0.05 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=3719.353, Time=0.05 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=3847.085, Time=0.01 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=3706.728, Time=0.09 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=3708.279, Time=0.14 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=3708.484, Time=0.19 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=3706.790, Time=0.09 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=3787.504, Time=0.13 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=3710.683, Time=0.15 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=3704.999, Time=0.06 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=3717.547, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=3800.850, Time=0.03 sec ARIMA(2,1,1)(0,0,0)[0] : AIC=3706.542, Time=0.10 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=3706.752, Time=0.10 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=3705.050, Time=0.05 sec ARIMA(2,1,0)(0,0,0)[0] : AIC=3785.510, Time=0.04 sec ARIMA(2,1,2)(0,0,0)[0] : AIC=3708.952, Time=0.12 sec Best model: ARIMA(1,1,1)(0,0,0)[0] Total fit time: 1.476 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2836.495, Time=0.01 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2723.898, Time=0.05 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2631.301, Time=0.05 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2834.495, Time=0.01 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2632.099, Time=0.08 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=2632.139, Time=0.07 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=2632.599, Time=0.10 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=2629.465, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=2630.231, Time=0.04 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=2630.270, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=2721.898, Time=0.02 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=2630.773, Time=0.06 sec Best model: ARIMA(0,1,1)(0,0,0)[0] Total fit time: 0.544 seconds Performing stepwise search to minimize aic ARIMA(0,0,0)(0,0,0)[0] intercept : AIC=1997.391, Time=0.01 sec ARIMA(1,0,0)(0,0,0)[0] intercept : AIC=1799.119, Time=0.03 sec ARIMA(0,0,1)(0,0,0)[0] intercept : AIC=1855.272, Time=0.04 sec ARIMA(0,0,0)(0,0,0)[0] : AIC=2004.016, Time=0.01 sec ARIMA(2,0,0)(0,0,0)[0] intercept : AIC=1798.751, Time=0.05 sec ARIMA(3,0,0)(0,0,0)[0] intercept : AIC=1798.996, Time=0.06 sec ARIMA(2,0,1)(0,0,0)[0] intercept : AIC=1801.445, Time=0.17 sec ARIMA(1,0,1)(0,0,0)[0] intercept : AIC=1799.266, Time=0.06 sec ARIMA(3,0,1)(0,0,0)[0] intercept : AIC=1798.950, Time=0.11 sec ARIMA(2,0,0)(0,0,0)[0] : AIC=1798.759, Time=0.03 sec Best model: ARIMA(2,0,0)(0,0,0)[0] intercept Total fit time: 0.558 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=3277.566, Time=0.01 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=3209.211, Time=0.09 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=3102.421, Time=0.05 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=3275.566, Time=0.01 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=3103.186, Time=0.07 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=3102.967, Time=0.08 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=3101.034, Time=0.16 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=3102.683, Time=0.18 sec ARIMA(1,1,3)(0,0,0)[0] intercept : AIC=3102.721, Time=0.21 sec ARIMA(0,1,3)(0,0,0)[0] intercept : AIC=3103.045, Time=0.11 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=3103.778, Time=0.14 sec ARIMA(2,1,3)(0,0,0)[0] intercept : AIC=3104.556, Time=0.41 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=3099.196, Time=0.07 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=3101.139, Time=0.04 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=3101.356, Time=0.05 sec ARIMA(2,1,2)(0,0,0)[0] : AIC=3100.830, Time=0.13 sec ARIMA(1,1,3)(0,0,0)[0] : AIC=3100.869, Time=0.12 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=3100.566, Time=0.02 sec ARIMA(0,1,3)(0,0,0)[0] : AIC=3101.182, Time=0.06 sec ARIMA(2,1,1)(0,0,0)[0] : AIC=3101.915, Time=0.08 sec ARIMA(2,1,3)(0,0,0)[0] : AIC=3102.708, Time=0.34 sec Best model: ARIMA(1,1,2)(0,0,0)[0] Total fit time: 2.432 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2983.292, Time=0.01 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2871.569, Time=0.06 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2792.319, Time=0.07 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2981.292, Time=0.01 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2794.178, Time=0.11 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=2794.196, Time=0.08 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=2795.205, Time=0.14 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=2790.605, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=2792.447, Time=0.04 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=2792.467, Time=0.04 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=2869.570, Time=0.01 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=2793.466, Time=0.07 sec Best model: ARIMA(0,1,1)(0,0,0)[0] Total fit time: 0.681 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2828.003, Time=0.01 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2749.845, Time=0.04 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2652.810, Time=0.04 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2826.020, Time=0.01 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2653.735, Time=0.07 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=2653.690, Time=0.07 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=inf, Time=0.29 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=2652.641, Time=0.03 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=2653.723, Time=0.04 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=2653.676, Time=0.05 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=2747.907, Time=0.02 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=inf, Time=0.21 sec Best model: ARIMA(0,1,1)(0,0,0)[0] Total fit time: 0.902 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2932.055, Time=0.01 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2850.398, Time=0.04 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2734.649, Time=0.06 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2930.055, Time=0.01 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2736.643, Time=0.08 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=2736.642, Time=0.07 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=2738.647, Time=0.09 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=2732.774, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=2734.769, Time=0.05 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=2734.768, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=2848.398, Time=0.02 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=2736.772, Time=0.05 sec Best model: ARIMA(0,1,1)(0,0,0)[0] Total fit time: 0.555 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2723.212, Time=0.01 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2588.926, Time=0.05 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2518.601, Time=0.04 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2721.212, Time=0.01 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2518.839, Time=0.08 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=2519.224, Time=0.07 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=2519.469, Time=0.11 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=2516.601, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=2516.839, Time=0.06 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=2517.224, Time=0.04 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=2586.926, Time=0.02 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=2517.469, Time=0.06 sec Best model: ARIMA(0,1,1)(0,0,0)[0] Total fit time: 0.577 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2595.168, Time=0.01 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2518.297, Time=0.04 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2410.902, Time=0.04 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2593.168, Time=0.01 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2412.579, Time=0.11 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=2412.533, Time=0.07 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=2414.166, Time=0.15 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=2408.902, Time=0.03 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=2410.579, Time=0.05 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=2410.533, Time=0.05 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=2516.297, Time=0.03 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=2412.166, Time=0.09 sec Best model: ARIMA(0,1,1)(0,0,0)[0] Total fit time: 0.694 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=2884.760, Time=0.01 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2838.736, Time=0.04 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2720.576, Time=0.08 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=2882.760, Time=0.01 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=2715.389, Time=0.13 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=2713.033, Time=0.15 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=2807.078, Time=0.08 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=2712.981, Time=0.17 sec ARIMA(3,1,0)(0,0,0)[0] intercept : AIC=2784.642, Time=0.08 sec ARIMA(4,1,1)(0,0,0)[0] intercept : AIC=2713.937, Time=0.23 sec ARIMA(3,1,2)(0,0,0)[0] intercept : AIC=2713.431, Time=0.28 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=2711.932, Time=0.33 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=2715.264, Time=0.15 sec ARIMA(2,1,3)(0,0,0)[0] intercept : AIC=2710.845, Time=0.33 sec ARIMA(1,1,3)(0,0,0)[0] intercept : AIC=2713.760, Time=0.35 sec ARIMA(3,1,3)(0,0,0)[0] intercept : AIC=2714.769, Time=0.50 sec ARIMA(2,1,4)(0,0,0)[0] intercept : AIC=2712.845, Time=0.40 sec ARIMA(1,1,4)(0,0,0)[0] intercept : AIC=2714.040, Time=0.23 sec ARIMA(3,1,4)(0,0,0)[0] intercept : AIC=2713.761, Time=0.53 sec ARIMA(2,1,3)(0,0,0)[0] : AIC=2708.927, Time=0.21 sec ARIMA(1,1,3)(0,0,0)[0] : AIC=2711.808, Time=0.29 sec ARIMA(2,1,2)(0,0,0)[0] : AIC=2709.972, Time=0.24 sec ARIMA(3,1,3)(0,0,0)[0] : AIC=2709.573, Time=0.36 sec ARIMA(2,1,4)(0,0,0)[0] : AIC=2710.926, Time=0.30 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=2713.350, Time=0.10 sec ARIMA(1,1,4)(0,0,0)[0] : AIC=2712.085, Time=0.18 sec ARIMA(3,1,2)(0,0,0)[0] : AIC=2711.468, Time=0.27 sec ARIMA(3,1,4)(0,0,0)[0] : AIC=2711.816, Time=0.40 sec Best model: ARIMA(2,1,3)(0,0,0)[0] Total fit time: 6.435 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=3008.357, Time=0.01 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=2987.978, Time=0.04 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=2891.598, Time=0.09 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=3006.357, Time=0.01 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=inf, Time=0.23 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=inf, Time=0.21 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=inf, Time=0.30 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=2889.601, Time=0.03 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=2865.911, Time=0.06 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=2985.978, Time=0.03 sec ARIMA(2,1,1)(0,0,0)[0] : AIC=2857.696, Time=0.09 sec ARIMA(2,1,0)(0,0,0)[0] : AIC=2956.233, Time=0.02 sec ARIMA(3,1,1)(0,0,0)[0] : AIC=2857.721, Time=0.13 sec ARIMA(2,1,2)(0,0,0)[0] : AIC=2850.007, Time=0.18 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=2860.445, Time=0.09 sec ARIMA(3,1,2)(0,0,0)[0] : AIC=2861.456, Time=0.25 sec ARIMA(2,1,3)(0,0,0)[0] : AIC=2794.774, Time=0.39 sec ARIMA(1,1,3)(0,0,0)[0] : AIC=2859.594, Time=0.24 sec ARIMA(3,1,3)(0,0,0)[0] : AIC=2853.848, Time=0.30 sec ARIMA(2,1,4)(0,0,0)[0] : AIC=inf, Time=0.62 sec ARIMA(1,1,4)(0,0,0)[0] : AIC=2860.187, Time=0.17 sec ARIMA(3,1,4)(0,0,0)[0] : AIC=inf, Time=0.56 sec ARIMA(2,1,3)(0,0,0)[0] intercept : AIC=2796.644, Time=0.46 sec Best model: ARIMA(2,1,3)(0,0,0)[0] Total fit time: 4.518 seconds
In [70]:
plotARIMAfunc(train_df_dundee, test_df_dundee, fit_df_dundee, forecast_df_dundee, lower_df_dundee, upper_df_dundee)
RMSE for ***TEST SITE*** Charge Your Car HQ Stations: 13.72907031779763 RMSE for Ardler Complex, Dundee Stations: 8.685406417161747 RMSE for Balunie Drive, Dundee Stations: 14.431368470096057 RMSE for Brington Place Sheltered Housing, Dundee Stations: 5.032932687422627 RMSE for DCC Environment, 34 Harefield Road Stations: 3.2930921132329536e-05 RMSE for Dock Street, Dundee Stations: 21.02145175602944 RMSE for Dundee House, Dundee Stations: 266.8385088781542 RMSE for Dundee Ice Arena, Dundee Stations: 101.82604186357524 RMSE for Earn Cresent, Dundee Stations: 0.06286407814376119 RMSE for Gellatly Street Car Park, Dundee Stations: 26.465802611983094 RMSE for Greenmarket Multi Car Park, Dundee Stations: 42.85239838509775 RMSE for Housing Office East, Dundee Stations: 18.487433778364913 RMSE for Housing Office West, Dundee Stations: 10.687982771081426 RMSE for Janet Brougham House, Dundee Stations: 4.972380071165433e-05 RMSE for Lochee Charging Hub, Dundee Stations: 266.53964299479054 RMSE for Marchbanks, Dundee Stations: 22.112810812087943 RMSE for Menziehill House, Dundee Stations: 9.242159960879269 RMSE for Mitchell Street, Dundee Stations: 4.52652238134178 RMSE for Nethergate, Dundee Stations: 12.649834624521548 RMSE for Oakland Day Centre, Dundee Stations: 9.791448103063336 RMSE for Olympia Multi-Storey Car Park, Dundee Stations: 16.5176569008321 RMSE for Princes Street Charging Hub Stations: 245.74283795308918 RMSE for Public Works Dept, Clepington Rd. Dundee Stations: 47.050493956588575 RMSE for Queen Street Car Park, Broughty Ferry, Dundee Stations: 60.14782368232508 RMSE for Sinclair Street Stations: 3.5431039996844804e-10 RMSE for Sinclair Street, Dundee Stations: 0.6641645528581733 RMSE for Social Work Building, Jack Martin Way, Dundee Stations: 7.594767160131575 RMSE for South Tay Street Stations: 3.809719802964983e-11 RMSE for South Tay Street, Dundee Stations: 18.386813414035576 RMSE for Trades Lane Stations: 5.979936798238124e-08 RMSE for Trades Lane, Dundee Stations: 0.06399750075769692 RMSE for Turriff House Rannoch Road, Dundee Stations: 7.722791914761989 RMSE for University of Dundee, Nethergate, Dundee Stations: 1.6642761033885702 RMSE for Whitfield Centre, Dundee Stations: 24.110184088487763
Perth¶
In [71]:
df_1 = pd.read_csv('data/EV_ChargeStation_Use_Sept_2016_to_Aug_2017.csv', index_col=[0]).drop(columns=['OBJECTID'])
df_2 = pd.read_csv('data/EVChargeStationUseSept2017toAug2018.csv', index_col=[0])
df_3 = pd.read_csv('data/EVChargeStationUseSept2018toAug2019.csv', index_col=[0])
df_1 = df_1[df_1['Site'] != '***TEST SITE*** Charge Your Car HQ']
df_3 = df_3[df_3['Site'] != '***TEST SITE*** Charge Your Car HQ']
In [72]:
# Define a mapping dictionary for renaming
rename_mapping = {
'King Street Car Park, Crieff': 'King Street Car Park',
'Broxden Park & Ride, Perth': 'Broxden Park & Ride',
'Canal Street Car Park 3rd floor, Perth': 'Canal Street Car Park',
'Canal Street Car Park 3rd floor ': 'Canal Street Car Park',
'Friarton Depot, Perth': 'Friarton Depot',
'South Inch Car Park, Perth': 'South Inch Car Park',
'Kinross Park and Ride, Kinross': 'Kinross Park and Ride',
' Leslie Street Car Park, Blairgowrie': 'Leslie Street Car Park, Blairgowrie',
}
# Replace the values in the 'Site' column using the mapping
df_1['Site'] = df_1['Site'].replace(rename_mapping)
df_2['Site'] = df_2['Site'].replace(rename_mapping)
df_3['Site'] = df_3['Site'].replace(rename_mapping)
df_1 = df_1.rename(columns={
'CP_ID': 'CP ID',
'Start_Date': 'Start Date',
'Start_Time': 'Start Time',
'End_Date': 'End Date',
'End_Time': 'End Time',
'Total_kWh': 'Total kWh'
})
# Union data
data_perth = pd.concat([df_1, df_2, df_3]).drop_duplicates()
# Drop records with below 0 Total kWh
data_perth = data_perth[data_perth['Total kWh'] >= 0]
# Drop two stations (too little data)
data_perth = data_perth[data_perth['Site'] != 'Market Square Alyth']
data_perth = data_perth[data_perth['Site'] != 'Mill Street, Perth']
In [73]:
data_perth.head()
Out[73]:
| CP ID | Connector | Start Date | Start Time | End Date | End Time | Total kWh | Site | Model | |
|---|---|---|---|---|---|---|---|---|---|
| _id | |||||||||
| 1 | 51519 | 2 | 2017/08/31 00:00:00 | 22:12:00 | 2017/08/31 00:00:00 | 23:11:00 | 18.27 | Broxden Park & Ride | APT Triple Rapid Charger |
| 2 | 51250 | 1 | 2017/08/31 00:00:00 | 22:01:00 | 2017/08/31 00:00:00 | 22:31:00 | 19.45 | Crown Inn Wynd Car Park, Auchterarder | Siemens Triple Rapid Charger |
| 3 | 50575 | 2 | 2017/08/31 00:00:00 | 21:21:00 | 2017/08/31 00:00:00 | 21:59:00 | 19.71 | South Inch Car Park | APT Triple Rapid Charger |
| 4 | 51516 | 2 | 2017/08/31 00:00:00 | 20:43:00 | 2017/08/31 00:00:00 | 21:03:00 | 9.84 | Kinross Park and Ride | APT Triple Rapid Charger |
| 5 | 50994 | 2 | 2017/08/31 00:00:00 | 19:50:00 | 2017/08/31 00:00:00 | 20:50:00 | 14.17 | Leslie Street Car Park, Blairgowrie | APT Triple Rapid Charger |
In [74]:
data_perth = data_perth.assign(timestamp=pd.to_datetime(data_perth["Start Date"]).dt.date)
data_perth = data_perth[["timestamp", "Site", "Total kWh"]].groupby(["timestamp", "Site"], as_index=False).sum()
data_perth = pd.pivot_table(data_perth, values="Total kWh", index="timestamp", columns= "Site", aggfunc=np.sum, fill_value=0)
data_perth.reset_index(inplace=True)
In [75]:
data_perth
Out[75]:
| Site | timestamp | Atholl Street Car Park, Dunkeld | Broxden Park & Ride | Canal Street Car Park | Crown Inn Wynd Car Park, Auchterarder | Friarton Depot | King Street Car Park | Kinross Park and Ride | Leslie Street Car Park, Blairgowrie | Moness Terrace Car Park, Aberfeldy | Rie-Achan Road Car Park, Pitlochry | South Inch Car Park |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 2016-01-09 | 0.000 | 111.820 | 0.000 | 0.000 | 35.370 | 0.000 | 42.435 | 13.234 | 0.000 | 40.436 | 23.946 |
| 1 | 2016-01-10 | 0.000 | 134.360 | 0.000 | 0.380 | 0.000 | 25.172 | 83.798 | 0.000 | 42.324 | 44.970 | 43.408 |
| 2 | 2016-01-11 | 0.000 | 90.670 | 0.000 | 0.000 | 35.930 | 100.149 | 68.370 | 35.475 | 0.000 | 19.590 | 35.115 |
| 3 | 2016-01-12 | 0.000 | 105.014 | 0.000 | 0.000 | 45.780 | 4.030 | 134.090 | 61.890 | 6.800 | 20.240 | 10.278 |
| 4 | 2016-02-09 | 0.000 | 59.211 | 0.000 | 5.820 | 0.000 | 0.000 | 56.630 | 9.540 | 0.000 | 18.610 | 36.482 |
| ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... | ... |
| 1090 | 2019-12-04 | 39.174 | 198.414 | 10.064 | 35.979 | 47.753 | 31.058 | 116.072 | 0.000 | 90.670 | 107.430 | 100.320 |
| 1091 | 2019-12-05 | 59.682 | 107.571 | 0.000 | 49.180 | 0.000 | 83.894 | 236.344 | 5.822 | 149.029 | 45.470 | 54.210 |
| 1092 | 2019-12-06 | 29.338 | 189.394 | 50.008 | 73.523 | 72.499 | 72.792 | 263.845 | 29.646 | 38.923 | 100.370 | 100.715 |
| 1093 | 2019-12-07 | 15.440 | 342.782 | 30.845 | 55.829 | 20.380 | 33.170 | 227.842 | 8.430 | 84.198 | 177.090 | 101.669 |
| 1094 | 2019-12-08 | 67.789 | 227.317 | 37.519 | 112.902 | 34.740 | 106.708 | 295.120 | 59.715 | 55.391 | 71.044 | 33.350 |
1095 rows × 12 columns
In [76]:
print(data_perth[data_perth == 0].count(axis=0)/len(data_perth.index))
Site timestamp 0.000000 Atholl Street Car Park, Dunkeld 0.369863 Broxden Park & Ride 0.000000 Canal Street Car Park 0.187215 Crown Inn Wynd Car Park, Auchterarder 0.103196 Friarton Depot 0.210959 King Street Car Park 0.053881 Kinross Park and Ride 0.003653 Leslie Street Car Park, Blairgowrie 0.075799 Moness Terrace Car Park, Aberfeldy 0.136986 Rie-Achan Road Car Park, Pitlochry 0.037443 South Inch Car Park 0.008219 dtype: float64
In [77]:
train_df_perth, test_df_perth, fit_df_perth, forecast_df_perth, lower_df_perth, upper_df_perth = autoARIMAfunc(data_perth)
Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=10030.742, Time=0.02 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=9811.805, Time=0.09 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=9518.750, Time=0.13 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=10028.747, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=9493.592, Time=0.31 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=9494.064, Time=0.57 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=inf, Time=0.93 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=9495.736, Time=0.29 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=9688.353, Time=0.16 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=9495.704, Time=0.61 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=9495.701, Time=0.11 sec Best model: ARIMA(1,1,1)(0,0,0)[0] intercept Total fit time: 3.232 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=12032.604, Time=0.02 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=11765.218, Time=0.11 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=11493.862, Time=0.17 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=12030.605, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=11473.533, Time=0.31 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=11467.721, Time=0.49 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=11699.774, Time=0.06 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=11469.337, Time=0.62 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=11469.393, Time=0.59 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=11493.244, Time=0.28 sec ARIMA(3,1,0)(0,0,0)[0] intercept : AIC=11651.560, Time=0.10 sec ARIMA(3,1,2)(0,0,0)[0] intercept : AIC=11469.468, Time=0.59 sec ARIMA(2,1,1)(0,0,0)[0] : AIC=11470.368, Time=0.20 sec Best model: ARIMA(2,1,1)(0,0,0)[0] intercept Total fit time: 3.554 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=9762.363, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=9515.295, Time=0.10 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=9145.777, Time=0.18 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=9760.363, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=9142.473, Time=0.27 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=9144.369, Time=0.34 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=9144.344, Time=0.38 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=9142.385, Time=0.27 sec ARIMA(0,1,3)(0,0,0)[0] intercept : AIC=9144.352, Time=0.35 sec ARIMA(1,1,3)(0,0,0)[0] intercept : AIC=9146.380, Time=0.39 sec ARIMA(0,1,2)(0,0,0)[0] : AIC=9143.411, Time=0.09 sec Best model: ARIMA(0,1,2)(0,0,0)[0] intercept Total fit time: 2.422 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=10637.850, Time=0.02 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=10324.212, Time=0.11 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=9982.715, Time=0.15 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=10635.857, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=9983.967, Time=0.28 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=9984.033, Time=0.28 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=9986.351, Time=0.42 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=9982.903, Time=0.04 sec Best model: ARIMA(0,1,1)(0,0,0)[0] intercept Total fit time: 1.316 seconds Performing stepwise search to minimize aic ARIMA(0,0,0)(0,0,0)[0] intercept : AIC=9120.514, Time=0.01 sec ARIMA(1,0,0)(0,0,0)[0] intercept : AIC=9109.434, Time=0.04 sec ARIMA(0,0,1)(0,0,0)[0] intercept : AIC=9108.063, Time=0.18 sec ARIMA(0,0,0)(0,0,0)[0] : AIC=10083.023, Time=0.01 sec ARIMA(1,0,1)(0,0,0)[0] intercept : AIC=9106.086, Time=0.30 sec ARIMA(2,0,1)(0,0,0)[0] intercept : AIC=9107.265, Time=0.57 sec ARIMA(1,0,2)(0,0,0)[0] intercept : AIC=9107.262, Time=0.51 sec ARIMA(0,0,2)(0,0,0)[0] intercept : AIC=9107.887, Time=0.20 sec ARIMA(2,0,0)(0,0,0)[0] intercept : AIC=9109.159, Time=0.11 sec ARIMA(2,0,2)(0,0,0)[0] intercept : AIC=9099.778, Time=0.98 sec ARIMA(3,0,2)(0,0,0)[0] intercept : AIC=9108.466, Time=0.43 sec ARIMA(2,0,3)(0,0,0)[0] intercept : AIC=9101.676, Time=1.06 sec ARIMA(1,0,3)(0,0,0)[0] intercept : AIC=9097.091, Time=0.83 sec ARIMA(0,0,3)(0,0,0)[0] intercept : AIC=9106.576, Time=0.23 sec ARIMA(1,0,4)(0,0,0)[0] intercept : AIC=9098.405, Time=1.02 sec ARIMA(0,0,4)(0,0,0)[0] intercept : AIC=9107.527, Time=0.40 sec ARIMA(2,0,4)(0,0,0)[0] intercept : AIC=inf, Time=1.22 sec ARIMA(1,0,3)(0,0,0)[0] : AIC=9110.793, Time=0.42 sec Best model: ARIMA(1,0,3)(0,0,0)[0] intercept Total fit time: 8.518 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=11353.305, Time=0.02 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=11142.981, Time=0.09 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=10780.862, Time=0.23 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=11351.305, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=inf, Time=0.38 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=inf, Time=0.38 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=10766.075, Time=0.35 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=10761.116, Time=0.48 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=inf, Time=0.79 sec ARIMA(3,1,2)(0,0,0)[0] intercept : AIC=inf, Time=0.69 sec ARIMA(2,1,3)(0,0,0)[0] intercept : AIC=inf, Time=0.84 sec ARIMA(1,1,3)(0,0,0)[0] intercept : AIC=10761.554, Time=0.63 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=inf, Time=0.48 sec ARIMA(3,1,3)(0,0,0)[0] intercept : AIC=10764.544, Time=1.10 sec ARIMA(2,1,2)(0,0,0)[0] : AIC=10765.260, Time=0.31 sec Best model: ARIMA(2,1,2)(0,0,0)[0] intercept Total fit time: 6.765 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=11805.941, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=11550.350, Time=0.06 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=11320.050, Time=0.14 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=11803.941, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=11290.265, Time=0.32 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=11281.184, Time=0.35 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=11477.699, Time=0.06 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=11282.657, Time=0.48 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=11282.225, Time=0.86 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=11280.668, Time=0.52 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=11296.598, Time=0.29 sec ARIMA(1,1,3)(0,0,0)[0] intercept : AIC=11282.251, Time=0.93 sec ARIMA(0,1,3)(0,0,0)[0] intercept : AIC=11285.276, Time=0.42 sec ARIMA(2,1,3)(0,0,0)[0] intercept : AIC=11281.473, Time=0.99 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=11287.691, Time=0.26 sec Best model: ARIMA(1,1,2)(0,0,0)[0] intercept Total fit time: 5.762 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=10400.723, Time=0.02 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=10163.676, Time=0.07 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=9887.935, Time=0.12 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=10398.725, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=9869.780, Time=0.23 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=9869.747, Time=0.35 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=10091.309, Time=0.07 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=9871.112, Time=0.47 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=9871.461, Time=0.65 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=9870.381, Time=0.35 sec ARIMA(3,1,0)(0,0,0)[0] intercept : AIC=10046.114, Time=0.11 sec ARIMA(3,1,2)(0,0,0)[0] intercept : AIC=9873.747, Time=0.39 sec ARIMA(2,1,1)(0,0,0)[0] : AIC=9868.433, Time=0.18 sec ARIMA(1,1,1)(0,0,0)[0] : AIC=9868.434, Time=0.11 sec ARIMA(2,1,0)(0,0,0)[0] : AIC=10089.319, Time=0.04 sec ARIMA(3,1,1)(0,0,0)[0] : AIC=9869.781, Time=0.29 sec ARIMA(2,1,2)(0,0,0)[0] : AIC=9870.141, Time=0.38 sec ARIMA(1,1,0)(0,0,0)[0] : AIC=10161.682, Time=0.03 sec ARIMA(1,1,2)(0,0,0)[0] : AIC=9869.061, Time=0.21 sec ARIMA(3,1,0)(0,0,0)[0] : AIC=10044.123, Time=0.07 sec ARIMA(3,1,2)(0,0,0)[0] : AIC=9872.433, Time=0.25 sec Best model: ARIMA(2,1,1)(0,0,0)[0] Total fit time: 4.409 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=10634.333, Time=0.02 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=10327.814, Time=0.07 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=9942.499, Time=0.19 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=10632.334, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=9944.307, Time=0.27 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=9944.314, Time=0.26 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=9946.487, Time=0.25 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=9945.072, Time=0.06 sec Best model: ARIMA(0,1,1)(0,0,0)[0] intercept Total fit time: 1.143 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=11473.581, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=11148.381, Time=0.09 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=10861.176, Time=0.16 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=11471.581, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=10858.734, Time=0.33 sec ARIMA(2,1,1)(0,0,0)[0] intercept : AIC=10849.066, Time=0.72 sec ARIMA(2,1,0)(0,0,0)[0] intercept : AIC=11055.925, Time=0.08 sec ARIMA(3,1,1)(0,0,0)[0] intercept : AIC=10849.518, Time=0.82 sec ARIMA(2,1,2)(0,0,0)[0] intercept : AIC=10861.988, Time=0.52 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=10862.543, Time=0.31 sec ARIMA(3,1,0)(0,0,0)[0] intercept : AIC=11035.948, Time=0.08 sec ARIMA(3,1,2)(0,0,0)[0] intercept : AIC=10845.396, Time=0.67 sec ARIMA(4,1,2)(0,0,0)[0] intercept : AIC=10846.827, Time=0.77 sec ARIMA(3,1,3)(0,0,0)[0] intercept : AIC=10847.006, Time=0.70 sec ARIMA(2,1,3)(0,0,0)[0] intercept : AIC=10848.396, Time=0.90 sec ARIMA(4,1,1)(0,0,0)[0] intercept : AIC=10846.639, Time=0.93 sec ARIMA(4,1,3)(0,0,0)[0] intercept : AIC=10848.777, Time=1.20 sec ARIMA(3,1,2)(0,0,0)[0] : AIC=10845.774, Time=0.36 sec Best model: ARIMA(3,1,2)(0,0,0)[0] intercept Total fit time: 8.696 seconds Performing stepwise search to minimize aic ARIMA(0,1,0)(0,0,0)[0] intercept : AIC=11115.758, Time=0.03 sec ARIMA(1,1,0)(0,0,0)[0] intercept : AIC=10819.519, Time=0.14 sec ARIMA(0,1,1)(0,0,0)[0] intercept : AIC=10436.160, Time=0.28 sec ARIMA(0,1,0)(0,0,0)[0] : AIC=11113.760, Time=0.02 sec ARIMA(1,1,1)(0,0,0)[0] intercept : AIC=10437.169, Time=0.51 sec ARIMA(0,1,2)(0,0,0)[0] intercept : AIC=10437.208, Time=0.43 sec ARIMA(1,1,2)(0,0,0)[0] intercept : AIC=10439.555, Time=0.46 sec ARIMA(0,1,1)(0,0,0)[0] : AIC=10438.854, Time=0.07 sec Best model: ARIMA(0,1,1)(0,0,0)[0] intercept Total fit time: 1.943 seconds
In [78]:
plotARIMAfunc(train_df_perth, test_df_perth, fit_df_perth, forecast_df_perth, lower_df_perth, upper_df_perth)
RMSE for Atholl Street Car Park, Dunkeld Stations: 57.56484821375761 RMSE for Broxden Park & Ride Stations: 72.02142375123651 RMSE for Canal Street Car Park Stations: 21.910401718878102 RMSE for Crown Inn Wynd Car Park, Auchterarder Stations: 34.11999425969723 RMSE for Friarton Depot Stations: 19.21460844219384 RMSE for King Street Car Park Stations: 36.018682504483664 RMSE for Kinross Park and Ride Stations: 61.77410729734898 RMSE for Leslie Street Car Park, Blairgowrie Stations: 38.43702496064899 RMSE for Moness Terrace Car Park, Aberfeldy Stations: 37.22802828762869 RMSE for Rie-Achan Road Car Park, Pitlochry Stations: 50.55069573338147 RMSE for South Inch Car Park Stations: 40.86241878616647
